The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X  0 X^3 X^2+X X^3+X^2+X X^3+X^2 X^2 X^3+X X^3+X X^3+X^2 X^2 X^3+X^2
 0  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3
 0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0  0  0 X^3
 0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3

generates a code of length 23 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+89x^20+304x^22+256x^23+283x^24+80x^26+10x^28+1x^44

The gray image is a linear code over GF(2) with n=184, k=10 and d=80.
This code was found by Heurico 1.16 in 0.032 seconds.